gambling_problems_simple

gambling_problems_simple.py

import random


# Set configuration in simulate() function


def naturals():
    n = 0
    while True:
        yield n
        n += 1


def sim_game(idx, p, Smin, Smax, k):
    for num_tosses in naturals():
        if num_tosses==0:
            continue  # skip zero
        r = random.uniform(0, 1)
        k += (1 if r < p else -1)  # +1 if winning toss
        win_game = k==Smax
        if k==Smin or win_game:
            break
    #print(f"idx={idx}: End with {num_tosses} tosses. Win: {win_game}")
    return num_tosses, win_game


def simulate():
    p = 0.5
    Smin = 0
    k = 25
    Smax = 30
    NUM_SIMS = 10000

    wins = 0
    win_num_tosses = 0
    for idx in range(NUM_SIMS):
        num_tosses, win_game = sim_game(idx, p, Smin, Smax, k)
        if win_game:
            wins += 1
            win_num_tosses += num_tosses

    win_rate = wins / NUM_SIMS
    win_num_tosses_rate = win_num_tosses / NUM_SIMS
    analytic_win_rate = 1 - p_ruin_analytic(p, Smin, Smax, k)

    print(f"\twin_rate: {win_rate}")
    print(f"\twin_num_tosses_rate: {win_num_tosses_rate}")
    print(f"\tanalytic_win_rate: {analytic_win_rate}")
    print(f"\tdiff: {win_rate - analytic_win_rate}")


def p_ruin_analytic(p, Smin, Smax, k):  # for comparison with the simulation
    """
    :param p: Propabity of gain per transition for player.
    :param Smin: Upper bound / goal.
    :param Smax: Ruin.
    :param k: Beginning capital owned by player.
    """
    assert not Smin, "Smin must be 0." # TODO: generalize
    assert Smin <= k <= Smax
    if p==1:
        return 0
    if p==1/2:
        return 1 - k / Smax
    q = 1 - p
    r = p / q
    num = r**(Smax - k) - 1
    denom = r**(Smax - 0) - 1
    return num / denom


if __name__=="__main__":
  
    simulate()